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Rachel98
 2 years ago
I don't really get this.
Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2
Rachel98
 2 years ago
I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

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mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0Do you mean a rigorous formal proof?

Rachel98
 2 years ago
Best ResponseYou've already chosen the best response.0I don't really know. This is what the question was and I don't get it.

mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0Do you understand how to use logarithms?

mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0Ah, you will want to understand natural logarithms for this question, I can explain it.

mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0\[y = \log_b x\] \[x = b^y\]

mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0If we take the natural logarithm of \[512^{\frac{2}{3}}\] \[\frac{2}{3}\ln(512)\]

mjr632
 2 years ago
Best ResponseYou've already chosen the best response.0We can pull the exponent out

Rachel98
 2 years ago
Best ResponseYou've already chosen the best response.0So, is that a cube root? That we ended up with?

precal
 2 years ago
Best ResponseYou've already chosen the best response.1yes they are both equivalent

Rachel98
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks, so much. That makes sense now.

precal
 2 years ago
Best ResponseYou've already chosen the best response.1no need to use logs here

ghass1978
 2 years ago
Best ResponseYou've already chosen the best response.1just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal
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